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N-Methyl Inversion Barriers in Six-membered Rings.

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N Methyl Inversion Barriers in Six-membered Rings[***
By Alan R. Katritzky, Ranjan C. Patel, and Frank G. Riddell[*]
Conformational conversions of N-methylazacyclohexanes are of particular interest: they
can proceed either via ring- or nitrogen-inversion processes. In both procedures an equatonal N-methyl group is converted into an axial one, and the converse. It is appropriate to
dissociate the energy barriers for N-methyl inversion into two "half-barriers" for the steps,
axial form -+ transition state and equatorial form -+ transition state, and to report both values separately. -In this article the N-methyl inversion barriers of numerous methylated
oligoazacyclohexanes, including species with oxygen or nitrogen atoms in the ring, are discussed.
1. Introduction
Since the fifties, conformational analysis has revolutionized our treatment of saturated ring systems. At first it was
applied mainly to carbocyclic systems, but its influence has
long been felt in saturated and partially saturated heterocyclic ring systems.
The substitution of a nitrogen or oxygen atom for a carbon atom in cyclohexane does not fundamentally change
the geometry. However, a trivalent nitrogen atom displays
the phenomenon of N-inversion. The N-substituent in a piperidine, for example, can occupy either the equatorial or
axial position, and there are two possible ways of these
conformations interconverting, either by ring- o r N-inversion.
tude of the N-inversion bamer in this compound and that
for other N-alkyl groups in other azacyclohexanes has
proved a fascinating and contentious problem.
The problems raised by studies of N-inversion barriers
in six-membered rings such as N-methylpiperidine (I)
have been a subject of dispute between the authors' laboratories[". Since the dates of the original communications
on this subject, much further work has been carried out by
each of our groups and by others and the principal points
of controversy now appear to have been resolved. This review outlines our agreed assessment of the current situation.
An important basic point is that the N-inversion bamer
cannot be measured by current NMR techniques for the
simplest six-membered derivative N-methylpiperidine (I).
This arises because the free energy difference between the
two conformations (le) and (la)is ca. 2.7 kcal/mol"', making it impossible to record peaks from the minor conformer (la) below the anticipated coalescence temperature,
even with the most sophisticated modem instrumentation"'.
Me
In the case of piperidine itself, the position of the equilibrium was long controversial, but this matter has now been
largely cleared up and the general view accepted that the
N-equatorial conformer predominates by a rather small
factor"]. For N-alkylpiperidines, it has long been accepted
that the N-equatorial form predominates, but the magni-
The only current technique that would appear to be
available for the measurement of the barrier in Kmethylpiperidine is ultrasonic relaxation; this has recently been
used with success, e.g. in studies of rotation in ethanesp'.
An ultrasonic relaxation study on N-methylpiperidine by
W p J o n e s et
in 1975 yielded a barrier of 6.0 kcal/mol
for the ax-+ts barrier1"'. Although A e measured by this
[*I Prof. Dr. A. R. Katritzky I"L Dr. R C. Patel
School of Chemical Sciences, University of East Anglia
Nonvich, NR4 7 T J (England)
Lk.F. G. Xiddell
Depaltment of Chemistry, The University
Stirling, FK9 4LA (Scotland)
['I Author to whom correspondence should be addressed. New address:
Deparment of Chemistry,
University of Florida,
Gainesville. Florida 3261 1 (USA)
[**I Conformational Analysis of Saturated Heterocycles, Part 9B.-Part 97:
A . R. Katriizky. R . C. Patel. F. G. Ridden. J. Chem. SOC.Chem. Commun. 1979,674,
Angew. Chem. Int. Ed. Engl. 20. S21-529 0981)
I*]
Given A@-2.7 kcal/mol and an optimistic upper temperature limit of
- 150"C at which N-inversion might be frozen out, the equilibrium constant
K is M. 65000 ( i e . ca. 2'6). Therefore, if a piece of information from the
(preferred) (Ie)completely filled one 16 bit word of store, only one bit would
be recorded in a word of store containing tbe corresponding information
from (In).Moreover these vaIues would be superimposed on noise certainly
greatly exceeding 1 hit in magnitude and would have no statistical significance. The problem is therefore beyond any 16 bit FT computer and probaTcomputers
bly beyond the dynamic range of the FT routines of all current I
utilizing larger word sizes.
[**I The following abbreviations are used: -axial,
eq-equatorial,
fs-transition state; KMethyl orientation: a- axial, e= equatorial.
8 Verlag Cheniie Gmbff, 6940 Weinheim. 1981
0570-0833/81/0707-0S21$ 52.50/0
521
technique was found to be 0.9 kcal/mol, a value much
lower than that currently acceptedl3],it is agreed that AH"
values from spectroscopic methods are more reliable than
those from ultrasonic relaxation techniques, whereas AGC
determinations compare well with reliable values from
other methods141.This suggests a AG' value of 6.0 kcal/
mol for the ux- ts barrier in N-methylpiperidine (1).
2. Measurement of Individual Half-Barriers
by NMR
A fundamental point arises in the interpretation of
NMR coalescence data. The rate constant obtained from
an NMR experiment is always the sum of the forward and
reverse rate constants, but three cases can be distinguished:
1. If the process being observed is the freezing out of a
biased equilibrium where K is e.g. 10, the observed rate
constant is effectively the greater of the two and therefore
corresponds to the conversion of the least stable conformer
in the transition state. This applies in all applications of
dynamic 13C-NMR line-broadening (Anet equations).
2. If there are appreciable concentrations of the two conformers of which the equilibration is being observed, the
individual activation energies can be obtained from the average AG' measured, and the A@ for the system, using
the equations derived by Bovey et ~ 1 . ' ~ ' .
3 . If the equilibrium under study is between two identical (or mirror image) conformers, then the measured rate
constant is for ground state transition state, and this applies regardless of the possible occurrence of minor
amounts of other conformers along the reaction coordinate.
It is obviously necessary to state clearly which "half-barrier" is referred to and the neglect of this has led to much
of the confusion in the literature.
-
3. Previous Interpretation of N-Inversion Barriers
It is now clear that our viewpoints[21can in many features be reconciled, if the work from Norwich'2a1is referred
to the change axial to transition state (ax- ts), whereas the
work from Stirling12b1
is referred to the change equatorial
to transition state (eq- ts). This viewpoint emphasizes the
fact that each nitrogen inversion barrier has to be formally
regarded as made up of two half-barriers (ax-ts and
eq- IS). Clearly, the difference between the two half-barriers represents the conformational energy difference of
the N-substituentl'l.
In their original preliminary communication, the Norwich group took the measured AG' of 6.8 kcal/mol, for
nitrogen inversion in the seven-membered N-methylhomopiperidine (2)[71, as a model (Table 1) to obtain empirical
increments for the quantitative interpretation of changes in
[*I In this analysis, the two observable quantities A G and AC' are represented by three parameters. This situation would clearly be better defined if
in future authors clearly specified to which direction their barriers referred.
Preferably both half barriers should be quoted.
522
N-inversion barriers in terms of changes in steric and electronic factors resulting from insertion of heteroatoms in
six-membered ringsc2"].It was concluded that p-heteroatoms significantly increased the atomic inversion barrier
(positive 0-heteroatom effect) and that a-heteroatoms had
still greater barrier enhancing effects. The barrier observed
for 2-methyl- 1-oxa-2-azacyclohexane (31, originally assigned to N-inversion'", was suggested to be due to ring inversion because the derived empirical increments predicted the N-inversion barrier to be much lower than that
observed.
Table 1. Model compounds used in incremental analyses
Compound
(21
(5)
(6)
6.8
[71
9.7
1111
8.1
8.4
I141
1131
(7)
(8)
~
AC: [kcal/mol]
Ref.
6.5
"51
This work was criticized by Riddell and Labaziewicz'2bl,
who noted that the seven-membered ring model (2) for Ninversion in N-methylpiperidine (1) was inadequate because it lacked the constraints imposed upon nitrogen inversion by a six-membered ring"]. The barrier in 2-methylI-oxa-2-azacyclohexane (3) was reasserted to be due to Ninversion and this has been verified r e ~ e n t l y ~ ~
It , is
' ~now
~.
clear that this barrier of ca. 13.7 kcal/mol (14.4 kcall
mol["]) applies to eq-rs, whereas the ax+ts barrier is
< 10.0 kcal/mol, thus explaining the misassignrnent by the
Norwich group. The Stirling workers suggested12b1
an alternative empirical analysis, which led to a barrier of 9.63
kcal/mol for the N-inversion barrier in N-methylpiperidine (I). It was concluded that b-heteroatoms have a marked
barrier decreasing effect and the N-inversion barriers reported[".'21 for compounds (5) and (61, which at the time
appeared to fall close to this derived value, were cited to
support this analysis.
However, these supplementary results for (5) and (6)
quoted by Riddell et al. can no longer be regarded as satisfactory. The N-inversion barrier of 9.7 kcal/mol in the
naphthalene derivative (5) was considered by Anderson
and Oehlschlugerc"l to reflect a distorted saturated sixmembered ring, for which N-inversion rates are measurable, because strain forces the C-N-C
angle apart in the
transition state and leads to distortion of the aromatic
rings. We conclude that (5) represents a strained model for
eq-rs N-inversion, with probably more strain in the ts
than the ground state; hence, the unstrained eq- ts barrier
[*I
N-Methyl homopiperidine (2) is expected to be biased to the conformation with the N-methyl group pseudo-equatorial.
Anyew. Chem. In!. Ed. Enyl. 20, 521-529 (1981)
in N-methylpiperidine should be significantly less than 9.7
kcal/mol. A study"31 of the tetrahydroisoquinoline (7)
gives 8.4 kcal/mol for N-inversion. In this compound,
strain that arises from opening of the C-N-C
angle in
the transition state is less than for (5); compound (7), therefore, probably provides a closer estimate of the eq- ts barrier in (I) than (5) permits.
n
4. Strained Piperidines
Although the equatorial conformation of 1,2,2,6-tetramethylpiperidine (9) is only favored by A = 1.9 kcal/mol
(cf-A@= 2.7 kcal/mol for N-methylpiperidine), both halfbarriers are considerably higher than those of N-methylpiperidine. Destabilization of the transition state with three
eclipsed methyl groups is evidently much greater than the
destabilizing torsional and van der Waals interactions of
the three adjacent equatorial methyl groups in the equatorial conformation (Scheme 1).
r
The barrier for the bicyclo[3.3.l]nonane derivative (6)
has been accurately measured by Nelsen et ~ 1 . " ~ 'as
8.11 f0.04 kcal/mol, whereas Lehn's previously "unpublished" proton data for (6)[lZ1(determined at - 80+-IOOC),
AG: =9.5 f 1.0 kcal/mol, was quoted by Riddell as support for his results[zb1.The variance with Nelsen's 13CNMR result was probably due to difficulties in accurately
determining data from the strongly coupled proton spectra. Moreover, we now agree that (6)is not a good model
since the methyl group is equatorial in one ring but axial in
the other. The barrier in the bicyclo[2.2.2]octane (8) has
been measured"" by Nelsen to be 6.5 kcal/mol. Nelsen
concluded that (6) has a higher barrier than (8) due to the
difficulty in expanding the C-N-C
angle to 120" for nitrogen inversion in (6) because of the rigid bicyclic system.
Taking the best of the available data from other workers,
and considering results from our own laboratories, we suggest that the best estimations for the barriers to N-inversion in N-methylpiperidine are AG+ (ax.+ ts)=6.0 kcal/
mol and A G' (eq- ts) = 8.7 kcaVmo1. These conclusions
take into account the cu. 2.7 kcal/mol AC' in favor of the
equatorial form of N-methylpipe15dine[~].
A general but basic point, that needs consideration before discussion of the various systems, is the applicability
of AGf values from coalescence data in any comparative
analysis. The barriers we are discussing range from cu. 6 to
cu. 15 kcal/mol over a correspondingly large temperature
range. If a nitrogen inversion process had an entropy of
activation appreciably different from zero, AG+ would
vary with temperature, making comparison of data obtained at different temperatures inappropriate. However,
all recent carefully determined"0,'6-'81 values of AS' for
nitrogen inversion processes fall in the range O k 2 . 5 cal
mol-' K - ' rendering AGf values a relatively good and reliable means of comparing activation energies. Finally, it
was not clear that incremental schemes of the type proposed by us are at all satisfactory for the analysis of substituent effects in anything but a qualitative sense. Riddell et
u I . ~ 'have
~ ' shown how dependent these schemes can be on
one selected piece of data and that additivity of substituent
effects does not hold in certain cases.
The data presently available on N-inversion barriers in
N-methylated six-membered nitrogen-containing rings are
collected in Table 2. Where possible, both ux+ts and
eq+ ts half barriers are given: there is generally an experimental error of f 0.2 kcal/mol in coalescence determinations of AG+.
Angew. Chem. Int. Ed. Engl. 20, 521-529 (1981)
l*
Scheme 1
For the piperidines with fused benzene rings, [2-methyltetrahydroisoquinoline (7) and the naphthalene derivative
(5)], only the eq- ts barriers are known. Compared with 1methylpiperidine this is marginally lower in (7), but considerably raised in (5) by the strain involved in expanding
the C-N-C
bond angle to the 120" required for pyramidal N-inversion.
The bridged azabicyclononane (6) has its N-methyl
group axial with respect to one ring and equatorial with respect to the other in each conformer: the measured barrier
should therefore be compared to ax- ts for piperidine, and
is considerably raised by the strain in the transition state.
For N-methyltropane (10)the strain is still greater in the
transition state and the ax-. ts barrier is raised by 3.2 kcall
mol: however, some strain is now found in the eq ground
state and thus eq-ts is only raised by 1.4 kcal/mol. The
barrier found for the azabicyclooctane (8) is near that for
ax+ ts in N-methylpiperidine: this molecule, with boatrings, is not strictly comparable with the others but evidently differential strains cancel in ground and transition
states.
5. 1,4-Di- and 1,3,5-Triheteracyclohexanes
Compared with N-methylpiperidine, the axial conformation ground state of 1,3-heteraazacyclohexanes is stabilized by (i) removal of a B-syn-axial proton, (ii) the generalized anomeric effect and (iii) for the S-N-heterocycles, by
further alleviation of syn-axial van der Waals interaction,
by the greater S-N transannular distance. The equatorial
conformation is destabilized by the anomeric effect and, in
the case of sulfur-nitrogen heterocycles, also by torsional
effects'"]. The transition state is also probably destabilized
by N(p) - X(sp3) lone pair-lone pair interaction (see
Scheme 2).
r
-I*
Scheme 2.
523
Taken together, these interactions should increase the
,Me
ux-+fs bamer (positive /3-heteroatom effect) but decrease
the eq-+ rs bamer (negative 8-heteroatom effect), compared
to corresponding values for N-methylpiperidine. This conclusion amalgamates ideas from both the original analyses"], and is amply borne out by the bamers for the three
parent compounds ( I ] ) ) , (12) and (13): ax-+ts=7.0-7.8
and eq- ts=7.9-7.1 kcal/mol (Table 2 ) ; for l-methylpiperidine a x 4 ts= 6.0 and eq-, ts= 8.7 kcab'mol). A similar
trend observed for l-oxa-2-aza-4-heteracyclohexanes
when
compared with 2-methyl-I-oxa-2-azacyclohexane(3), is
discussed below.
For methylated 1,3,5-triheteracyclohexanes, the interconversion path must be defined. Two intermediates are
possible: 1. the conformer with no axial methyl groups (ee)
or 2. the conformer with two axial methyl groups (aa).
Which intermediate is involved has no effect on the interpretation, since the measured barrier is that for me-+ ts [for
(14)] or ae-, t s [for (IS)].However, there are also two possible transition states (Fig. 1): t, should have a higher energy
than f,, due to greater electronic interactions; thus pathway (2), via intermediate aa,is more likely. It follows that
the measured bamers are eq-rfs, and once again we
clearly see the effects of the /3-heteroatoms in lowering the
eq-fs barriers (TabIe 2). The ux-trs bamers are not experimentally accessible, but they must be lower than those
for eq+rs (see Fig. 1); however, in these cases the axial
ground state has two syn-axial methyl groups and is hence
itself of rather high energy.
0Me
WMe
ae
ee
0:"
N7-
LW
He/ ea
aa
ae
Fig. 1 Conformational equilibria of l,3,5-trimethyI-1,3,5-triazacyclohexane
(14) (Z- NMe) and 3,5-dim~hyl-l-oxa-3,5-diazacyclohtxane
(15) (Z=O).
Values in kcal/mol.
The high N-inversion barriers for trans-l,4,5,8-tetraazadecaIin (I7), a 'I ,3-diazacyciohe~ane"*~,
reflect additional
transition state strain from (i) eclipsing methyl-methyl, (ii)
p-sp3 lone pair-lone pair ('passing') interactions, and (iii)
rigidity of the trans-ring junction. Still higher bamers are
found for the bicycl~2.2.2)octylhydrazines (26)L'51
(AGZ=
1'1 Although not strictly a I,3-diheteracyclohexane,the interactions in (17)
are similar and are conveniently considered here. E. Furhs. S. Weinmun. U.
Schrnueli. A. R. Kutrifzky. R. C.Putel. unpublished results.
524
Angew. Chem. Int. Ed. Engl. 20. 521-529 (1981)
Table 2. Half-bamers for N-methyl inversion in six-membered heterocycles.
Comp.
Ring
Subst.
T,rC]
Pipendine
Homopiperidine
(I)
(2)
Strained Fiperidines
(5)
Dihydro-2-azaphenalene
(6)
9-Azabicyclo[3.3.1]nonane
(7)
Tetrahydroisoquinoline
(8)
2-Azabicyclo(2.2.2~tane
(9)
Piperidine
(10)
Nortropane
I-Me
I-Me
DNMR-data
AG,'
Rocess
kcal/mol]
-
-
Half-barriers
Footeq-ts
note
[kcal/ moll
ax-Is
6.0
-
2.7 (e)
6.8
e+ e'
U
U
72
9.7
U
8.1
8.4
6.5
9.1
9.2
e+ d
a+ d
e + e'
n+d
a+ e
a- e
U
- 9o
- 99
- 127
7.0
7.5
7.1
7.2
6.8
ea-ee
e-a
e- a
aee+ aae+ aee'
ae c aa z ea
9.1
aeae+ eaea
-125
2-Me
9-Me
2-Me
2-Me
1,2,2,6-Mea
N-Me
Ref.
A@ [a1
[kcal/mol]
-
-
60
40
8.7
6.8
9.7
8.1
0.0
8.1
U
U
8.4
6.5
11.0
6.5
9. I
9.2
0.0
1.9 (e)
0.9 (e)
10.1
1.3-Di-and 1,3.5-TriheteracycIohexanes
(11)
(12)
(13)
(14)
(15)
(16)
(1 7)
1.3-Diazacyclohexane
I-Oxa-3-azacyclohexane
1-Thia-3-azacyclohexane
1J,5-Triazacyclohexane
I-Oxa-3,5-diazacyclohexane
1,3-Dioxa-5-azacyclohexane
rrans-l,4,5.8-Tetraazadecalin
1,3-Mez
3-Me
3-Me
1,3,5-Me3
3,5-Me2
5-Me
1,4,5,8-Me4
-120
- 115
-115
- 120
- 130
- 71
-
-
7.0
7.6
7.8
< 7.2
4 6.8
0.9 (ee)
0.1 ( a )
0.7 (a)
-
-
>2.0 ( a )
0.0
7.9
7.5
7.1
7.2
6.8
-
9.1
9.1
1.3-Diheteracyclohexanes with equatorial C-methyl groups a to N-methyl groups
(IS)
1,3-Diazacyclohexane
Perhydro-1,4,7,%tetraazaphenalene
I-Oxa-3-azacycloheaane
1-0xa-3-azacyclohexane
I-Oxa-3-azacycloheaane
(19)
(20)
(2 1)
(22)
1,2,3-Me3 cu. - I05
8.0
eee- aee
0.9 (nee)
8.0
7.1
1,2,4,5,7,8-Me6 - 103
23-Me2
-110
3,4-Me2
- 105
2,3,4-Me3
- 95
8.0
7.6
7.6
8.0
eaa- aaa
ea- ee
ee-ae
eee+ eae
0.4 (aaa)
0.05 (ee)
0.1 (ae)
0.8 (eae)
8.3
7.6
7.7
8.8
7.9
7.65
7.6
8.0
- 30
11.6
1.6
12.0
8. I
12.7
12.2
7.9
13.7
ea- ee
ae+ aa+ ea
ea- pe
aa+ ea
ea- ee
ae +ea
0.4 (ee)
211.6
0.0
< 6.0
7.6
U
112.0
< 6.0
12.6
12.2
1.9
r 12.0
e+ d
33.7 ( e )
< 10.0
8.1
12.9
12.2
7.9
13.7
14.4
13.5
14.9
e+ e'
e+ d
a+ d
33.7 (e)
2-3.7
< 10.7
< 9.7
14.4
13.5
0.0
14.9
I,2-Diheteracyclohexanes
(23)
1J.-Diazacyclohexane
I,2-Me2
(24)
12-Diaza4-cyclohexene
1,2-Me2
(25)
(26)
rranr-2,3-Diazadecalin
2,3-Diazabicycl42.2.2~aane
1.2-DiazabicycloI2.2.2~ane
I-Oxa-2-azacyclohexane
4.4.5.5-TetradeuterioI -oxa-2-azacyclohexane
I-Oxa-2-ma-6cyclohexene
2-0aa-3-azabicycIof2.2.2]octane
23-Me2
2,3-Me2
2-Me
2-Me
(27)
(3)
(4)
(28)
(29)
j-
88
:;
f 2
- 7
-113
ca. f 5
2-CD3
2-Me
3-Me
f
f
+
5
2
22
a+
a'
0.0
0.3 fee)
0.0
0.0
3 12.0
U
1.2-Diheteracyclohexanes with a-C-methyl group(s)
(30)
1.ZDiazacyclohcxane
(31)
1,2-Diazacyclohexane
1.2-Diazacyclohexane
(32)
irons- 1,2,3,6
Me4
- 100
cu-1,2,3,6-Me4 - 20
1,2,33.6,6-Me6 - 23
ae+ aa+ ea
ae+ ad
ae+ ad
0.0
< 6.0
U
U
211.8
U
U
3 11.6
12.0
7.5
ae+ a&
U
2 12.0
ae+ aa+ ea
1.0 (ae)
U
< 6.0
12.4
6.8
ae+ ad
ae+ aa+ ea
U
12.6
6.9
ea+ ed
ae+ aa+ ea
U
0.9 (ae)
1.8
ae+ aa+ ea
ca.l.0 (ae)
7.9
11.8
11.6
7.9
1 , 2 , k T r i ~ r e r a r y ~ l o h ~ awith
n e ~two a4acent N-methyl groups
I J.4Triazacyclohexane
1-ntia-3,4-diazacyclohexane
-
3,4-Me2
5
{ U< 6.0
{ < 6.0
6.0
1.1 (ae)
C
1,2,6Triazacyclohexan
IJ,3,4-Me4
-
92
-
-
11.4
U
< 6.0
{ < 6.0
< 6.0
{C 6.0
I -Thia-3,4-diazacyclohexane
1-Thia-3,4diazacyclohexane
1.4-Dioxa-2-azacyclohexane
I -0xa-4-thia-2-azacyclohexane
1,4-Dioxa-2-azacyclohexane
I -0xa-4-thia-2-azacycbhexane
2.3,4Me,
2,2.3,4-Mc4
2-Me
2-Me
2,3,3-Me,
2,3,3-Me3
1-Oxa-2,5-diazacyclohexane
2,5-Me2
{ - 20
2,4-Mez
L 1 2
7.0
13.3
8.2
13.9
7.7
e+ e'
e+ e'
e+ e'
e+ e'
N-2 e+e'
N-5 e-a
N-2 a-e
N-4 a-e
N-2 e + d
N-5 a - e
N-2 e + d
N-5 a-e
1,2,4,5-Me4
- 19
trow
1,2.3,4,5,6-Me6 - 97
11.8
aaees eeaa
0.0
I391
7.7
aeae', eaea
0.0
1401
1-Oxa-2,4-diazacyclohexane
1-Oxa-2,5-diazacyclohexane
2,5,6-Me3
1-Oxa-2,5-dIazacyclohexane
2,5,6,6-Me4
-
- 39
-
11.5
11.7
11.9
14.6
7.7
45
- 13
{
11.1
;:
7.5
7.6
3 12.7
6.8
7.6
b 12.6
6.9
7.6
7.8
7.6
> 2 (ae)
> 2 (ae)
0.9 (e)
0.95 (e)
0.6 ( e )
0.3 (e)
10.6
11.1
11.6
< 10.9
7.9
11.1
7.0
U
8.2
< 10.2
7.7
11.4
11.5
11.7
11.9
14.6
7.6
12.7
7.8
3 13.3
8.3
13.9
8.2
b 10
311.8
10.5
U
0.3 (N-5 a)
1.6 (N-2 e)
0.8 (N-4 e) [381
ca.2.0
0.1 (N-5 e) [371
U
0.5 (N-5e) f371
1.2.4.5- Tetraheteracyclohexanes
(47)
(48)
[a] U
1,2,4,5-Tetraazacyclohexane
1,2,4,5-Te~etn~cyclohcxane
- unknown: letter in brackets denotes prefened conformer.
-
4
6.0
7.7
-
[b] Biased to N-methyl axial. [c] N-methyl axial. Id] Process cannot be unambiguously assigned. [el
AH+ = 15.1 20.4 kcal/rnol; AS+ -2.3+ 1.5 cal-' K - '_[fl 3,6-Me2 diequatorial. k]3,6-Me2 axial equatorial. [h] N-2-Inversion: N-4-methyl equatorial. [il See Fig. 2.
ti] N-I-lnvemion. [k] N-3-Inversion. n] N-CInversion. [m] Biased to N-3a-N-4 e. [n] A@ unknown, but probably 33.7 kcal/mol in favor of N-2 eq; cf. (3). [o] For
the high energy process, AH* = 14.4kO.l kcal/mol and AS+= - 1.2-tO.4 cat-' K - ' . [p] See Fig. 3.
12.2 kcal/mol), the intermediate methine unit in (17) obviously alleviates the mentioned interactions.
6. 1,3-Diheteracyclohexanes with Equatorial
C-Methyl Groups in a-Position to N-Methyl Groups
The data in Table 2 lead to the following conclusions: (i)
provided there are not more than two adjacent methyl
groups, the effect of C-methyl on the equilibria and kinetics of N-methyl is small [cf. (20) and (21) with (12): (ii)
three adjacent methyl groups raise ax-. ts barriers by 1.01.3 kcal/mol [cf. (18)and (19)with (11). and (22)with (12)]:
(iii) three adjacent methyl groups can considerably affect
eq-ts barriers, but the effect is variable (-0.8 to +0.5
kcal/mol for the two comparisons available).
Conclusions (ii) and (iii) can be rationalized in the following way: upon insertion of an a-equatorial C-methyl
group leading to three adjacent methyl groups, the energy
of the ground state for an equatorial N-methyl group is
raised, as well as that for the transition state (‘passing
Me-Me interactions’); the effect is least for the axial Nmethyl ground state. Comparison of the data (Table 2) for
1,3-dimethyl- (11) and I,2,3-trimethyl- 1,3-diazacyclohexane (18) shows that ts is raised by 1.0 and eq by 1.8 kcall
mol more than the ax ground state. A similar comparison
of 3-methyl- (12) and 2,3,4-trimethyl- I-oxa-3-azacyclohexane (22)gives the ts and eq raised by 1.2 and 1.8 kcal/mol,
respectively, more than the ax ground state. Finally, comparison of the tricyclic derivative (19) with (18) gives 0.3
and 1.3 kcal/mol respectively.
peridine. For the parent compound (23),only lower limits
are available for these barriers because of ambiguity with
ring inversion, but they are in good accord. For the unsaturated compound (24) a high passing barrier of 12.0 kcal/
mol cannot be unambiguously assigned, hence the passing
N-inversion barrier (ax-ts) is 3 12.0 kcal/mol.
The non-passing eq+ ts-barriers determined for the parent compounds (23) and (24) are, at 7.6 and 8.1 kcal/mol,
respectively, significantly lower than eq- ts for N-methylpiperidine; compound (30), with a single adjacent C-methy1 group, falls in the same range.
Only upper estimates for the non-passing ax+ ts barriers
can be given for (23). (24). and (30),as no signals were detected for the aa-conformers at low temperature: they may
not be very different from ax+ ts in N-methyl piperidine.
Only high passing N-inversion barriers are observed for
(31)and (32):the non-passing N-barrier for (32) is thought
to be < 7.6 kcal/m01~~~]
owing to destabilization of the aeground state by axial C-methyl groups.
8. 1-Oxa-2-azacyclohexanes
We now agree that AG’ = 14.4 kcal/mol found for the
parent N-methyl compound (3)IZb3
’*I arises from N-inversion, that it should be assigned to eq- ts (following NMR
criterion (iii), see Section 2), that the A@ is 33.7 kcal/
m ~ l ~ and
’ ~ ~that
, the ax-rts half-barrier is hence 6 10.7
kcal/mol. Therefore, compared to N-methylpiperidine, the
ax+ ts and eq-. ts half-barriers are raised by d 4.7 and 5.7
kcal/mol, respectively. Clearly, the transition state for inversion in (3) is raised by lone pair-lone pair interactions,
which are qualitatively similar to those found for the passing N-inversion in 1,2-dimethyl-1,2-diazacyclohexane(23)
(see Section 7) (Scheme 3).
e
n
7. 1,ZDiazacyclohexanes
The conformational analysis of these compounds, including their N-inversion barriers, has been authoritatively
reviewed by Nelsen1211and only a brief account will be
given here. The Norwich group originally pointed outLza.22J
that there were two different N-inversion barriers for these
compounds and this has now been amply
with a distinction being made between (i) low ‘non-passing’ barriers for N-methyl inversion when the adjacent Nmethyl group is axial and (ii) high ‘passing’ barriers when
the adjacent N-methyl group is equatorial. It was originally
believedfzz1that the high energy of the transition state for
the ‘passing’ barriers arose from steric methyl-methyl interactions, but later realizedL2“’
that the lone pair-lone pair interaction is mainly responsible (see detailed discussion in
12 1.231).
Nelsen’s
on the bicyclic derivative (25). for
which ring inversion is not possible, allows accurate determination of the ‘passing’ ax- ts and eq+ ts barriers as 12.6
and 12.9 kcal/mol, respectively; i. e. they are raised by 6.6
and 4.2 kcal/mol respectively, compared to N-methylpi-
526
Scheme 3.
The non-passing N-methyl inversion in 1,2-diazacyclohexane (23) has half-barrier energies not vastly different
from those of N-methylpiperidine (1): this indicates that
an a-equatorial lone pair has little effect on the transition
state energy. Hence, the major differences in half-barrier
energies between 1,2-diazacyclohexane (23) and 1-0xa-2azacyclohexane (3) are probably due to ground state energy variations. Quantitative comparison indicates that the
equatorial ground state in (3) is stabilized relative to (25)
by 1.5 kcal/mol and the axial ground state is destabilized
by >1.9 kcal/mol. The former effect is probably mainly
steric: loss of methyl-methyl interaction. The latter is certainly due to gain in unfavorable lone pair-lone pair interactions. Barriers in the unsaturated analogue (28) are
Angew. Chem. Int. Ed. Engl. 20, 521-529 (1981)
rather similar to those of (3). Manifestations of these effects are also observed in the bicyclooctanes (8) and (27),
and (26) and (29): lone pair-lone pair interactions and torsion effects in (27) lead to an increase of 1.4 kcal/mol for
the barrier to N-methyl inversion relative to (8). A similar
but greater increase (+ 2.7 kcal/mol) is found on proceeding from (26) to (29).
9. 1,2,4-Triheteracyclohexanes
with Two Adjacent NMethyl Groups
The 1,2,4-triheteracyclohexanes(33), (34). and (35) have
high passing barriers of > 13 kcal/mol: however, the passing N-inversion barriers cannot be distinguished unambiguously from the similar energy, passing ring inversion
barriers. The non-passing N-inversion barriers in these
compounds have been unequivocally determined and will
be discussed at length.
The relevant conformational equilibria for 1,2,4-trimethyl- 1,2,4-triazacyclohexane (33) are shown in Figure 2"'.
The measured barrier of 7.5 kcal/mol relates to the AG+
for the conversion of conformers ae and ea, where conformer ae is more stable by A @ = 1.0 kcal/mol (this is discussed in detail in [2s1). Conformers ae and ea are interconverted via the still less stable conformer aa, and thus AG+
could either refer to ea+aa/ea or to ea-+ae/aa,depending on whether aa/ea or ae/aa has the higher energy.
However, we can equate the energy difference (ae/aa- ae)
to the 7.6 kcal/mol barrier measured for the N-inversion of
1,2-dimethyl-1,2-diazacyclohexane(23)12'],because the yeffect is known to be small (vide infra). Hence, the observed AG' must refer to ea+aa/ea, and by difference,
the @-effectis calculated as a 1.1 kcal/mol raising of the
ax+ ts barrier aa+ aa/ea. The barrier aa+ ae/aa is presumably the same as in 1,2-dimethyl-1,2-diazacyclohexane,
IZ=NMel
6.9 101
75
t
ae
y 3
aa
ea
Fig. 2. Conformational equilibria for 1,2,4-trimethyl-l,2,4-triazacyclohexane
(33) [Z= NMe (eq)]; 3,4-dimethyl-l-oxa-3,4-diazacyclohexane
(35) [ Z = O ] :
and 3,4-dirnethyl-l-thia-3,4-diazacyclohexane(34) [Z= S ] . Values in kcal/
mol.
[*] We do not consider any conformers with an axial N-4-Methyl group: the
lowest energy of these (1 e2e4a)- and (I e2n4a)-conformers still have energies
above both a e and ea, and will not be involved in the ne-ea
sion.
Angew. Chem. lnr. Ed. Engl. 20, 521-529 (1981)
interconver-
for which we only have an upper limit < 6.0 kcal/mol. We
can now calculate A@ for the minor conformer aa as
0.9 kcal/mol. Similar conclusions follow for 3,4-dimethyl- 1-oxa- (35) and 3,4-dimethyl- I-thia-cyclohexane (34).
Figure 2 includes the values of A @ and AG' measured for
both of these compounds. The p-effects of the 0 and S heteroatoms raise the ax+ rs barrier aa- a d e a by 1.0 and 0.5
kcal/mol respectively. AG" for the minor conformers aa
are estimated as 2 1.1 and 20.7 kcal/mol, respectively. pEffects are observed for the N-2- and N-3-inversion, respectively for (33), (34), (35). as expected.
10. 1,2,4-Triheteracyclohexanes
without Two Adjacent N-Methyl Groups
We consider first the compounds with a single N atom.
The barriers in 2-methyl- 1,4-dioxa-2-azacyclohexane(39)
and 2-methyl-] -oxa-4-thia-2-azacyclohexane(40) can be
compared with those of (12) and (13) to demonstrate that
the effect of an a-oxygen atom is to raise the ax-ts and
eq+ ts barriers by 2.9 and 3.9 -4.5 kcal/mol, respectively.
This can be compared with the value of < 4.7 and 5.7 kcal/
mol for the effect of an a-oxygen on the barrier in N-methylpiperidine [cf. ( I ) and (3)]: additivity is evidently not
maintained. A further comparison can be made with 2-methyl- 1-oxa-2-azacyclohexane to determine the effect of a pheteroatom: this is found to lower the eq- ts barrier by 3.0
and 2.9 kcal/mol for oxygen and sulfur, respectively
[compare (3) with (39) and (40J; corresponding effects on
the ax--*ts barrier are certainly much smaller and probably
in the other direction, but cannot be calculated exactly.
The effects of adjacent geminal C-methyl groups on the
N-inversion in (39) and (40) is shown by compounds (41)
and (42) to raise ax- rs and eq- rs barriers by 0.6 - 1.0 and
0.3- 0.4 kcal/mol, respectively.
The N-2-inversion process in 2,5-dimethyl-l-oxa-2,5diazacyclohexane (43) shows that the y-nitrogen atom has
no noticeable effect: the eq-ts barrier is identical with
that of (3): in the C-methyl derivatives (45) and (46), analogously high barriers are found for the N-2-inversion
(13. I - 13.9 kcal/mol) showing the small effect of a-C-methyl groups.
Comparison of the N-2-inversion processes in 2,4-dimethyl-l-oxa-2,4-diazacyclohexane(44) and 1,3-dimethyl-1,3diazacyclohexane (11) shows that the a-oxygen atom increases the ax+ ts and eq- ts barriers by 4.1 and 4.8 kcal/
mol, respectively. Comparison with 2-methyl-I-oxa-2-azacyclohexane (3) indicates that the @-nitrogenatom in (44)
raises the ux+rs barrier by 20.4 and lowers the eq-ts
barrier by 1.7 kcal/mol (see Fig. 3).
The N-5-inversion barrier for 2,5-dimethyl-l-oxa-2,5diazacyclohexane (43) and the N-4-inversion barrier for
the 2,4-analogue (44) are, within 0.2 kcal/mol, identical to
the corresponding barriers in (12) and (II), respectively,
showing that the y-oxygen and y-nitrogen effects are negligible. The effect of a 6-methyl group in (45) or 6,6-gern dimethyl groups in (46) is almost zero for the ax+ rs barrier
but raises the eq-+rs barriers of (43) by 0.7 kcal/mol: the
former agree, but the latter is significantly greater than
those found in the corresponding pair (12)/(20).
521
gative p-heteroatom effect) barriers. These p-heteroatom
effects are rather regular: an equatorial p-N-methyl group
increases the ax- ts barrier by 1.0 kcal/mol, whereas p-oxygen and p-sulfur atoms have greater effects (+ 1.6 and
1.8 kcal/mol respectively). Similariy, the 0-heteroatom
effects on the eq+ t s barrier are respectively - 0.8, - 1.2,
and - 1.6 kcal/mol for eq N-Me, -0 and -S. The effects of
a-heteroatoms are less regular: axial a-N-methyl groups
significantly decrease the eq- fs barrier (ca. - 1.1 kcall
mol), their effect on the ax-+ts barrier is probably small.
By contrast, equatorial a - N-methyl groups and a-oxygen
atoms increase both the ax+ ts and eq-+ ts barriers by 2.9 6.6 kcal/mol : the effect of an equatorial a-N-methyl group
is greatest on the ax+ ts and that of an a-oxygen is greatest
on the eq-ts barrier.
a-C-methyl groups show small effects on the barriers,
unless either three methyl groups on adjacent ring atoms
result or a geminal dimethyl group is involved. In the
former case, the ax+ IS barriers are considerably increased,
but the effect is less regular on eq- ts. In the latter case the
reverse applies.
These effects are rationalized in terms of steric and electronic interactions.
+
--I--16
_--P--Me
Me
I
I
ELMe
d-f
Me-N-N--Me
ae
ee
N---N-/elp
d--J
ea
Fig. 3 . Conformational equilibria and kinetics for 2,4-dimethyl-l-oxa-2,4-diazacyclohexane (44). Values in kcal/mcl.
11. Tetraheteracyclohexanes
Interconversion of the mirror image form of syrn-tetramethyltetrazacyclohexane (47) (Scheme 4, left) involves
either (i) passing ring inversion and non-passing N-inversion or (ii) passing N-inversion. We therefore know that
the passing N-barrier eq- ts in (47) is 11.8 kcai/mol. It
would be expected to be similar to that for the 1,2,4-triazaanalogue (33) (12.0 kcal/mol).
Scheme 4
In the hexamethyl analogue (48) (Scheme 4, right), the
non-passing eq- ts barrier is 7.7 kcal/mol, almost identical
to the corresponding barrier of 7.9 kcal/mol for frans1,2,3,6-tetramethy1-1,2-diazacyclohexane
(30).
13. General Significance of Results
The concept of using “half-barriers’’ to describe conformational changes does not appear to have been much utilized in the past, but it is clearly of general applicability. In
principle, for any biased equilibrium the energy of the
transition state relative to the ground state depends on
which of the two (or more) ground states is considered as
reference. This applies, for example, to the conformational
equilibria of carbocyclic compounds, to inversion barriers
for acyclic pyramidial compounds containing a chiral center, and to many rotational barriers.
Underlining the importance of realization of this concept is the fact that different experimental measurements
are related to different ground states. General adoption of
the quotation of equilibrium interconversions in terms of
half-barriers, as described in the present paper, would be
helpful in avoiding ambiguity and confusion.
Received: January 2, 1980 [A 374 IE]
German version: Angew. Chem. 93, 567 (1981)
[I] I . D. Blackburne, A . R. Katritzky, Y. Takenchi, Acc. Chem. Res. 8, 300
12. Summary
Due to substantial and variable conformational bias, Ninversion barriers in six-membered rings must be discussed
in terms of the half-barriers ax+ts and eq-+ts. For N-methylpiperidine we have decided that AG+ (ax- ts) = 6.0
kcal/mol and AG’ (eq- ts) = 8.7 kcal/rnol.
y-Heteroatoms have negligible effects on both half-barriers (<0.2 kcal/mol). B-Heteroatoms increase the ax-, ts
(positive P-heteroatom effect), but decrease the eq-ts (ne-
528
(1975).
[2] a) I . J . Ferguson. A . R. Katritzky. D. M. Read, J. Chem. SOC.Chem.
Commun. 1975. 255; b) F. G. Riddell, ibid. H . Lobaziewicz 1975,766.
[3] a) F. A. L. Anet, I . Yauari, I . J. Ferguson. A . R. Katritzky, M. MorenoMarias. M . J. T. Robinson, J. Chem. SOC.Chem. Commun. 1976,399; h)
D. C. Appleton. J. McKenna. J. M . McKenna, L. B. Sims, A . R. Walley,
J. Am. Chem. SOC.98,292 (1976); c) P. J. Crowley, M . J. T. Robinson, M.
G. Ward, Tetrahedron 33,915 (1977).
[4] E. Wyn-Jones, R . A . Pethrick. Top. Stereochem. 5, 269 (1970).
[5] V. M. Gittins, P. J. Heywood, E. Wyn-Jones.J. Chem. SOC.Perkin Trans.
2 197s. 1642.
I61 F. A. Bouey, E . W . Anderson, F. P. Hood, R. L. Kornegay, J. Chem. Phys.
40,3099 (1964).
171 J. B. Lumbert, W. L. Oliver, Jr., B. S . Packard, J. Am. Chem. SOC.93,
933 (1971).
Angew. Chem. Int. Ed. Engl. 20, 521-529 (1981)
F. G. Riddell. J. M. Lehn. J. Wagner, Chem. Commun. 1968, 1403.
F. G. Riddell, J. E. Anderson, J . Chem. SOC.Perkin Trans. 2 1977, 588.
F. G. Riddell, E. S. Turner, A. Boyd, Tetrahedron 35, 259 (1979).
J . E. Anderson, A. C. Oehlschlager, Chem. Commun. 1968, 284.
[I21 J . M. Lehn, Fortschr. Chem. Forsch. IS, 311 (1970).
[I31 M. Dauis, H. M. Hiigel, R. Lakhan. B. Ternai. Aust. J . Chem. 29, 1445
(1976).
1141 S. F. Nelsen. G. R. Weisman, E. L. Cleman, V. E. Peacock, J. Am.
Chem. SOC.98, 6893 (1976).
1151 S. F. Nelsen. G. R. Weisman, J . Am. Chem. SOC.98, 1842 (1976).
1161 F. G. Riddell, A. J. Kidd. J. Chem. SOC.Perkin Trans. 2 1977, 1816.
[I71 D. Hofner, I. Tamir. G. Binsch, Org. Magn. Reson. 11, 172 (1978).
[I81 D. Hofner, S. A. Lesko, G. Binsch. Org. Magn. Reson. 11, 179 (1978).
1191 F G. Riddell. M . H . Berry, E. S. Turner, Tetrahedron 34, 1415 (1978).
I201 A. R. Katritzky, R. C. Patel, J . Chem. SOC.Perkin Trans. 2 1980, 279.
[21] S. F Nelsen, Acc. Chem. Res. 11. 14 (1978).
[22] R. A. Y. Jones, A. R. Katritzky, R. Scattergood, Chem. Commun. 1971,
644.
[23] G . R. Weisman, S. F. Nelsen, J. Am. Chem. SOC.98, 7007 (1976).
[24] S. F. Nelsen, G. R. Weisman,J . Am. Chem. SOC.98, 3281 (1976).
(251 A. R. Katritzky, R. C. Patel, J . Chem. SOC. Perkin Trans. 2 1979, 984.
1261 H.-J. Schneider, L. Stunn, Angew. Chem. 88,574 (1976); Angew. Chem.
Int. Ed. Engl. 15, 545 (1976).
[271 A. R. Katritzky. V. J. Baker, I. J . Ferguson. R. C. Patel, J. Chem. SOC.
Perkin Trans. 2 1979, 143.
[281 A. R. Katritzky. V. J. Baker, F. M. S. Brifo-Palma. J . Chem. SOC.Perkin
Trans. 2 1980, 1734.
181
[9]
[lo]
[l I]
1291 A. R. Katritzky. V. J. Baker, F. M.S. Brito-Palma, I. J . Ferguson, L. Angiolini, J. Chem. SOC.Perkin Trans. 2 1980, 1746.
1301 V. J . Baker, I. J . Ferguson. A. R. Katritzky. R. Patel, S. Rahimi-Rastgo.
J . Chern. SOC.Perkin Trans. 2 1978, 377.
[31] I. J. Ferguson. A. R. Katritzky, R. Patel, J . Chem. SOC.Perkin Trans. 2
1976, 1564.
I321 J. E. Anderson. J . Am. Chem. SOC.91,6374 (1969).
[33] A. R. Katritzky, R. C. Patel, D. M. Read, Tetrahedron Lett. 1977,
3803.
[34] I. J. Ferguson. A . R. Katritzky. D. M. Read, J. Chem. SOC.Perkin Trans.
2 1976, 1861: A . R. Katritzky, R. C. Patel, F. M . S. Brito-Palma. F. G.
Riddell, E. S. Turner, Isr. J . Chem. 29, 150 (1980).
[35] R. A. Y. Jones, A. R. Katritzky, A. R . Martin, S. Saba, J . Chem. SOC.Perkin Trans. 2 1974, 1561.
[36] A. R. Katritzky, R. C. Patel, F. G. RiddelI. E. S. Turner, unpublished results.
[37] A. R. Katritzky, R. C. Patel, Heterocycles 9,263 (1978); F. G. Riddell, E.
S. Turner, ibid. 9,267 (1978); A. R. Katritzky, R. C. Patel, 3. Chem. SOC.
.Perkin Trans. 2 1979,993; F. G. Riddell. E. S. Turner, J . Chem. Res. (S)
1978, 476.
[38] F. G. RiddeIl, E. S. Turner, Heterocycles 9, 267 (1978): F. G. Riddell, E.
S. Turner, A . R. Katritzky, R. C. Patel, F. M. S. Brito-Palma, Tetrahedron 35, 1391 (1979).
I391 V. J . Baker, A. R. Katritzky, J.-P. Majoral, A. R. Martin, 1. M. Sullivan,
J . Am. Chem. SOC.98, 5748 (1976).
1401 A. R. Katritzky, I. J. Ferguson, R. C. Patel, J . Chem. SOC.Perkin Trans. 2
1979,981.
Benzvalene- Properties and Synthetic Potential
By Manfred Christl[*'
Dedicated to Professor Siegfried Hiinig on the occasion of his 60th birthday
Today, thanks to the versatile synthesis developed by Katz et al., benzvalene is not only the
most extensively studied valence isomer of benzene but also one of the most easily synthesized bicycle[ 1.1.O]butane derivatives. The double bond in this highly strained hydrocarbon
is particularly reactive owing to interactions between the 0 system and the double bond.
Benzvalene is one of the most reactive olefins toward electron deficient substrates. Furthermore, the compound is bifunctional, since after addition to the TI system the ring strain of
the c system provides the driving force for rearrangement or further addition reactions.
This paper summarizes the spectroscopic properties and the reactivity of benzvalene. In order to demonstrate the importance of benzvalene and its derivatives as building blocks in
organic synthesis the chemistry of compounds arising from benzvalene is also discussed.
The article concludes with a summary of substituted benzvalenes.
1. Introduction
For the research chemist to be interested in a particular
compound, three important requirements must be met:
first, it must be easily accessible, it should be highly reactive, and the reaction products must show interesting properties. Cyclooctatetraene, norbornene and without doubt
benzvalene (I) are examples of compounds satisfying these
conditions.
[*I Prof. Dr. M. Christ1
Institut fur Organische Chemie der Universitgt
Am Hubland, D-8700 Wikrzburg (Germany)
Angew. Chem. Int. Ed. Engl. 20. 529-546 (1981)
(1)
The substituted derivatives (243)"l and (245)'*I (Section
4) were already known when in 1967 Wilzback et uI.'~] identified benzvalene ( I ) as a photoproduct of benzene. Four
years later, Katz et a1.[4.51
reported a versatile synthesis
starting from lithium cyclopentadiene, dichloromethane,
and methyllithium, which made it possible to obtain 20 g
quantities of (I). This opened up the way for intensive
studies of its physical and chemical properties and also
0 Verlag Chemie GmbH. 6940 Weinheim, 1981
0570-0833/81/0707-529% 02.50/0
529
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